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<h1 class="mume-header" id="%E6%9C%BA%E5%99%A8%E5%AD%A6%E4%B9%A0%E6%A8%A1%E5%9E%8B%E8%AF%84%E4%BC%B0indexhtml"><a href="./index.html">&#x673A;&#x5668;&#x5B66;&#x4E60;&#xFF1A;&#x6A21;&#x578B;&#x8BC4;&#x4F30;</a></h1>

<ul>
<li><a href="#%E6%9C%BA%E5%99%A8%E5%AD%A6%E4%B9%A0%E6%A8%A1%E5%9E%8B%E8%AF%84%E4%BC%B0indexhtml">&#x673A;&#x5668;&#x5B66;&#x4E60;&#xFF1A;&#x6A21;&#x578B;&#x8BC4;&#x4F30;</a>
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<li><a href="#%E6%8B%9F%E5%90%88">&#x62DF;&#x5408;</a>
<ul>
<li><a href="#%E8%BF%87%E6%8B%9F%E5%90%88overfitting">&#x8FC7;&#x62DF;&#x5408;&#xFF08;Overfitting&#xFF09;</a></li>
<li><a href="#%E6%AC%A0%E6%8B%9F%E5%90%88underfitting">&#x6B20;&#x62DF;&#x5408;&#xFF08;Underfitting&#xFF09;</a></li>
</ul>
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<li><a href="#%E6%A8%A1%E5%9E%8B%E8%AF%84%E4%BC%B0%E6%96%B9%E6%B3%95">&#x6A21;&#x578B;&#x8BC4;&#x4F30;&#x65B9;&#x6CD5;</a>
<ul>
<li><a href="#%E7%95%99%E5%87%BA%E6%B3%95hold-out">&#x7559;&#x51FA;&#x6CD5;&#xFF08;Hold-out&#xFF09;</a></li>
<li><a href="#%E4%BA%A4%E5%8F%89%E9%AA%8C%E8%AF%81%E6%B3%95cross-validation">&#x4EA4;&#x53C9;&#x9A8C;&#x8BC1;&#x6CD5;&#xFF08;Cross Validation&#xFF09;</a></li>
<li><a href="#%E8%87%AA%E5%8A%A9%E6%B3%95bootstrapping">&#x81EA;&#x52A9;&#x6CD5;&#xFF08;Bootstrapping&#xFF09;</a></li>
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<li><a href="#%E6%80%A7%E8%83%BD%E5%BA%A6%E9%87%8F">&#x6027;&#x80FD;&#x5EA6;&#x91CF;</a>
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<li><a href="#%E5%9B%9E%E5%BD%92%E9%97%AE%E9%A2%98">&#x56DE;&#x5F52;&#x95EE;&#x9898;</a>
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<li><a href="#%E5%9D%87%E6%96%B9%E8%AF%AF%E5%B7%AEmean-squared-error">&#x5747;&#x65B9;&#x8BEF;&#x5DEE;&#xFF08;Mean squared error&#xFF09;</a></li>
<li><a href="#%E5%B9%B3%E5%9D%87%E7%BB%9D%E5%AF%B9%E8%AF%AF%E5%B7%AEmean-absolute-error">&#x5E73;&#x5747;&#x7EDD;&#x5BF9;&#x8BEF;&#x5DEE;&#xFF08;Mean absolute error&#xFF09;</a></li>
</ul>
</li>
<li><a href="#%E5%88%86%E7%B1%BB%E9%97%AE%E9%A2%98">&#x5206;&#x7C7B;&#x95EE;&#x9898;</a>
<ul>
<li><a href="#cross-entropy">Cross Entropy</a></li>
</ul>
</li>
<li><a href="#%E9%94%99%E8%AF%AF%E7%8E%87%E4%B8%8E%E7%B2%BE%E5%BA%A6">&#x9519;&#x8BEF;&#x7387;&#x4E0E;&#x7CBE;&#x5EA6;</a></li>
<li><a href="#%E6%B7%B7%E6%B7%86%E7%9F%A9%E9%98%B5">&#x6DF7;&#x6DC6;&#x77E9;&#x9635;</a>
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<li><a href="#%E5%87%86%E7%A1%AE%E7%8E%87">&#x51C6;&#x786E;&#x7387;</a></li>
<li><a href="#%E7%89%B9%E5%BC%82%E5%BA%A6">&#x7279;&#x5F02;&#x5EA6;</a></li>
<li><a href="#%E7%B2%BE%E7%A1%AE%E7%8E%87%E6%9F%A5%E5%87%86%E7%8E%87">&#x7CBE;&#x786E;&#x7387;&#xFF08;&#x67E5;&#x51C6;&#x7387;&#xFF09;</a></li>
<li><a href="#%E5%8F%AC%E5%9B%9E%E7%8E%87%E6%9F%A5%E5%85%A8%E7%8E%87">&#x53EC;&#x56DE;&#x7387;&#xFF08;&#x67E5;&#x5168;&#x7387;&#xFF09;</a></li>
<li><a href="#%E5%B9%B3%E8%A1%A1%E7%82%B9bepbreak-even-point">&#x5E73;&#x8861;&#x70B9;&#xFF08;BEP&#xFF0C;Break-Even Point&#xFF09;</a></li>
<li><a href="#f_1"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>F</mi><mn>1</mn></msub></mrow><annotation encoding="application/x-tex">F_1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em;">F</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:-0.13889em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span></a></li>
<li><a href="#f_%CE%B2"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>F</mi><mi>&#x3B2;</mi></msub></mrow><annotation encoding="application/x-tex">F_&#x3B2;</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.969438em;vertical-align:-0.286108em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em;">F</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361079999999999em;"><span style="top:-2.5500000000000003em;margin-left:-0.13889em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.05278em;">&#x3B2;</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em;"><span></span></span></span></span></span></span></span></span></span></a></li>
<li><a href="#roc">ROC</a></li>
</ul>
</li>
</ul>
</li>
<li><a href="#%E4%BB%A3%E4%BB%B7">&#x4EE3;&#x4EF7;</a>
<ul>
<li><a href="#%E4%BB%A3%E4%BB%B7%E6%95%8F%E6%84%9Fcost-sensitive%E9%94%99%E8%AF%AF%E7%8E%87">&#x4EE3;&#x4EF7;&#x654F;&#x611F;&#xFF08;Cost-Sensitive&#xFF09;&#x9519;&#x8BEF;&#x7387;</a></li>
<li><a href="#%E4%BB%A3%E4%BB%B7%E6%9B%B2%E7%BA%BFcost-curve">&#x4EE3;&#x4EF7;&#x66F2;&#x7EBF;&#xFF08;Cost Curve&#xFF09;</a></li>
</ul>
</li>
<li><a href="#%E6%AF%94%E8%BE%83%E6%A3%80%E9%AA%8C">&#x6BD4;&#x8F83;&#x68C0;&#x9A8C;</a></li>
<li><a href="#%E5%81%8F%E5%B7%AE">&#x504F;&#x5DEE;</a></li>
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</li>
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<h2 class="mume-header" id="%E6%8B%9F%E5%90%88">&#x62DF;&#x5408;</h2>

<h3 class="mume-header" id="%E8%BF%87%E6%8B%9F%E5%90%88overfitting">&#x8FC7;&#x62DF;&#x5408;&#xFF08;Overfitting&#xFF09;</h3>

<p>&#x7565;</p>
<h3 class="mume-header" id="%E6%AC%A0%E6%8B%9F%E5%90%88underfitting">&#x6B20;&#x62DF;&#x5408;&#xFF08;Underfitting&#xFF09;</h3>

<p>&#x7565;</p>
<h2 class="mume-header" id="%E6%A8%A1%E5%9E%8B%E8%AF%84%E4%BC%B0%E6%96%B9%E6%B3%95">&#x6A21;&#x578B;&#x8BC4;&#x4F30;&#x65B9;&#x6CD5;</h2>

<h3 class="mume-header" id="%E7%95%99%E5%87%BA%E6%B3%95hold-out">&#x7559;&#x51FA;&#x6CD5;&#xFF08;Hold-out&#xFF09;</h3>

<p>&#x76F4;&#x63A5;&#x5C06;&#x6570;&#x636E;&#x96C6;&#x5212;&#x5206;&#x4E3A;&#x4E24;&#x4E2A;&#x4E92;&#x65A5;&#x5730;&#x96C6;&#x5408;&#xFF0C;&#x5176;&#x4E2D;&#x4E00;&#x4E2A;&#x96C6;&#x5408;&#x4F5C;&#x4E3A;&#x8BAD;&#x7EC3;&#x96C6;&#xFF0C;&#x53E6;&#x4E00;&#x4E2A;&#x4F5C;&#x4E3A;&#x6D4B;&#x8BD5;&#x96C6;&#x3002;&#x5728;&#x4F7F;&#x7528;&#x65F6;&#xFF0C;&#x4E00;&#x822C;&#x8981;&#x91C7;&#x7528;&#x82E5;&#x5E72;&#x6B21;&#x968F;&#x673A;&#x5212;&#x5206;&#xFF0C;&#x91CD;&#x590D;&#x8FDB;&#x884C;&#x5B9E;&#x9A8C;&#xFF0C;&#x8BC4;&#x4F30;&#x540E;&#x53D6;&#x5E73;&#x5747;&#x503C;&#x4F5C;&#x4E3A;&#x7ED3;&#x679C;&#x3002;</p>
<h3 class="mume-header" id="%E4%BA%A4%E5%8F%89%E9%AA%8C%E8%AF%81%E6%B3%95cross-validation">&#x4EA4;&#x53C9;&#x9A8C;&#x8BC1;&#x6CD5;&#xFF08;Cross Validation&#xFF09;</h3>

<p><img src="./images/e_CrossValidation.png" alt></p>
<h3 class="mume-header" id="%E8%87%AA%E5%8A%A9%E6%B3%95bootstrapping">&#x81EA;&#x52A9;&#x6CD5;&#xFF08;Bootstrapping&#xFF09;</h3>

<p>&#x5047;&#x5B9A;&#x5305;&#x542B;<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>m</mi></mrow><annotation encoding="application/x-tex">m</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em;"></span><span class="mord mathdefault">m</span></span></span></span>&#x4E2A;&#x6837;&#x672C;&#x7684;&#x6570;&#x636E;&#x96C6;<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>D</mi></mrow><annotation encoding="application/x-tex">D</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathdefault" style="margin-right:0.02778em;">D</span></span></span></span>&#xFF0C;&#x6BCF;&#x6B21;&#x4ECE;<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>D</mi></mrow><annotation encoding="application/x-tex">D</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathdefault" style="margin-right:0.02778em;">D</span></span></span></span>&#x4E2D;&#x968F;&#x673A;&#x6311;&#x9009;&#x4E00;&#x4E2A;&#x6837;&#x672C;&#xFF0C;&#x5C06;&#x5176;&#x62F7;&#x8D1D;&#x5165;<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mi>D</mi><mo mathvariant="normal" lspace="0em" rspace="0em">&#x2032;</mo></msup></mrow><annotation encoding="application/x-tex">D&apos;</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.751892em;vertical-align:0em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.02778em;">D</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.751892em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">&#x2032;</span></span></span></span></span></span></span></span></span></span></span></span>&#xFF0C;&#x91CD;&#x590D;<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>m</mi></mrow><annotation encoding="application/x-tex">m</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em;"></span><span class="mord mathdefault">m</span></span></span></span>&#x6B21;&#xFF0C;&#x5C31;&#x5F97;&#x5230;&#x4E86;&#x5305;&#x542B;<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>m</mi></mrow><annotation encoding="application/x-tex">m</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em;"></span><span class="mord mathdefault">m</span></span></span></span>&#x4E2A;&#x6837;&#x672C;&#x7684;&#x6570;&#x636E;&#x96C6;<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mi>D</mi><mo mathvariant="normal" lspace="0em" rspace="0em">&#x2032;</mo></msup></mrow><annotation encoding="application/x-tex">D&apos;</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.751892em;vertical-align:0em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.02778em;">D</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.751892em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">&#x2032;</span></span></span></span></span></span></span></span></span></span></span></span>&#x3002;&#x663E;&#x7136;&#xFF0C;<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>D</mi></mrow><annotation encoding="application/x-tex">D</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathdefault" style="margin-right:0.02778em;">D</span></span></span></span>&#x4E2D;&#x7684;&#x4E00;&#x90E8;&#x5206;&#x6837;&#x672C;&#x4F1A;&#x5728;<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mi>D</mi><mo mathvariant="normal" lspace="0em" rspace="0em">&#x2032;</mo></msup></mrow><annotation encoding="application/x-tex">D&apos;</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.751892em;vertical-align:0em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.02778em;">D</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.751892em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">&#x2032;</span></span></span></span></span></span></span></span></span></span></span></span>&#x4E2D;&#x591A;&#x6B21;&#x51FA;&#x73B0;&#xFF0C;&#x4E00;&#x90E8;&#x5206;&#x6837;&#x672C;&#x4E0D;&#x4F1A;&#x5728;<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mi>D</mi><mo mathvariant="normal" lspace="0em" rspace="0em">&#x2032;</mo></msup></mrow><annotation encoding="application/x-tex">D&apos;</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.751892em;vertical-align:0em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.02778em;">D</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.751892em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">&#x2032;</span></span></span></span></span></span></span></span></span></span></span></span>&#x4E2D;&#x51FA;&#x73B0;&#x3002;&#x8BE5;&#x65B9;&#x6CD5;&#x5728;&#x6570;&#x636E;&#x96C6;&#x8F83;&#x5C0F;&#xFF0C;&#x96BE;&#x4EE5;&#x6709;&#x6548;&#x5212;&#x5206;&#x8BAD;&#x7EC3;&#x96C6;&#x3001;&#x6D4B;&#x8BD5;&#x96C6;&#x65F6;&#x5F88;&#x6709;&#x7528;&#xFF0C;&#x4F46;&#x4F1A;&#x5F15;&#x5165;&#x4F30;&#x8BA1;&#x504F;&#x5DEE;&#x3002;</p>
<h2 class="mume-header" id="%E6%80%A7%E8%83%BD%E5%BA%A6%E9%87%8F">&#x6027;&#x80FD;&#x5EA6;&#x91CF;</h2>

<h3 class="mume-header" id="%E5%9B%9E%E5%BD%92%E9%97%AE%E9%A2%98">&#x56DE;&#x5F52;&#x95EE;&#x9898;</h3>

<h4 class="mume-header" id="%E5%9D%87%E6%96%B9%E8%AF%AF%E5%B7%AEmean-squared-error">&#x5747;&#x65B9;&#x8BEF;&#x5DEE;&#xFF08;Mean squared error&#xFF09;</h4>

<p><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mrow><mi mathvariant="normal">M</mi><mi mathvariant="normal">S</mi><mi mathvariant="normal">E</mi></mrow><mo stretchy="false">(</mo><mi>y</mi><mo separator="true">,</mo><mi>f</mi><mo stretchy="false">)</mo><mo>=</mo><mfrac><mrow><munderover><mo>&#x2211;</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mi>m</mi></munderover><mo fence="false">(</mo><msub><mi>y</mi><mi>i</mi></msub><mo>&#x2212;</mo><mi>f</mi><mo stretchy="false">(</mo><msub><mi>x</mi><mi>i</mi></msub><mo stretchy="false">)</mo><msup><mo fence="false">)</mo><mn>2</mn></msup></mrow><mi>m</mi></mfrac></mrow><annotation encoding="application/x-tex">\mathrm{MSE}(y, f) = \dfrac{
    \sum\limits_{i=1}^{m} \Big(y_i-f(x_i) \Big)^2
}{m}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord"><span class="mord mathrm">M</span><span class="mord mathrm">S</span><span class="mord mathrm">E</span></span><span class="mopen">(</span><span class="mord mathdefault" style="margin-right:0.03588em;">y</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathdefault" style="margin-right:0.10764em;">f</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:3.4076769999999996em;vertical-align:-0.686em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.7216769999999997em;"><span style="top:-2.668008em;"><span class="pstrut" style="height:3.354008em;"></span><span class="mord"><span class="mord mathdefault">m</span></span></span><span style="top:-3.584008em;"><span class="pstrut" style="height:3.354008em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-4.721677em;"><span class="pstrut" style="height:3.354008em;"></span><span class="mord"><span class="mop op-limits"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.3513970000000004em;"><span style="top:-2.122331em;margin-left:0em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span><span class="mrel mtight">=</span><span class="mord mtight">1</span></span></span></span><span style="top:-3.0000050000000003em;"><span class="pstrut" style="height:3em;"></span><span><span class="mop op-symbol small-op">&#x2211;</span></span></span><span style="top:-3.950005em;margin-left:0em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">m</span></span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.9776689999999999em;"><span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord"><span class="delimsizing size2">(</span></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.03588em;">y</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:-0.03588em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">&#x2212;</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathdefault" style="margin-right:0.10764em;">f</span><span class="mopen">(</span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mclose">)</span><span class="mord"><span class="mord"><span class="delimsizing size2">)</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:1.3540079999999999em;"><span style="top:-3.6029em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></p>
<ul>
<li>&#x4F18;&#x70B9;&#x662F;&#x4FBF;&#x4E8E;&#x68AF;&#x5EA6;&#x4E0B;&#x964D;&#xFF0C;&#x8BEF;&#x5DEE;&#x5927;&#x65F6;&#x4E0B;&#x964D;&#x5FEB;&#xFF0C;&#x8BEF;&#x5DEE;&#x5C0F;&#x65F6;&#x4E0B;&#x964D;&#x6162;&#xFF0C;&#x6709;&#x5229;&#x4E8E;&#x51FD;&#x6570;&#x6536;&#x655B;&#x3002;</li>
<li>&#x7F3A;&#x70B9;&#x662F;&#x53D7;&#x660E;&#x663E;&#x504F;&#x79BB;&#x6B63;&#x5E38;&#x8303;&#x56F4;&#x7684;&#x79BB;&#x7FA4;&#x6837;&#x672C;&#x7684;&#x5F71;&#x54CD;&#x8F83;&#x5927;</li>
</ul>
<h4 class="mume-header" id="%E5%B9%B3%E5%9D%87%E7%BB%9D%E5%AF%B9%E8%AF%AF%E5%B7%AEmean-absolute-error">&#x5E73;&#x5747;&#x7EDD;&#x5BF9;&#x8BEF;&#x5DEE;&#xFF08;Mean absolute error&#xFF09;</h4>

<p><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mrow><mi mathvariant="normal">M</mi><mi mathvariant="normal">A</mi><mi mathvariant="normal">E</mi></mrow><mo stretchy="false">(</mo><mi>y</mi><mo separator="true">,</mo><mi>f</mi><mo stretchy="false">)</mo><mo>=</mo><mfrac><mrow><munderover><mo>&#x2211;</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mi>m</mi></munderover><mo fence="false">&#x2223;</mo><msub><mi>y</mi><mi>i</mi></msub><mo>&#x2212;</mo><mi>f</mi><mo stretchy="false">(</mo><msub><mi>x</mi><mi>i</mi></msub><mo stretchy="false">)</mo><mo fence="false">&#x2223;</mo></mrow><mi>m</mi></mfrac></mrow><annotation encoding="application/x-tex">\mathrm{MAE}(y, f) = \dfrac{
    \sum\limits_{i=1}^{m} \Big| y_i-f(x_i) \Big|
}{m}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord"><span class="mord mathrm">M</span><span class="mord mathrm">A</span><span class="mord mathrm">E</span></span><span class="mopen">(</span><span class="mord mathdefault" style="margin-right:0.03588em;">y</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathdefault" style="margin-right:0.10764em;">f</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:3.4050659999999997em;vertical-align:-0.686em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.7190659999999998em;"><span style="top:-2.6653970000000005em;"><span class="pstrut" style="height:3.3513970000000004em;"></span><span class="mord"><span class="mord mathdefault">m</span></span></span><span style="top:-3.5813970000000004em;"><span class="pstrut" style="height:3.3513970000000004em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-4.719066em;"><span class="pstrut" style="height:3.3513970000000004em;"></span><span class="mord"><span class="mop op-limits"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.3513970000000004em;"><span style="top:-2.122331em;margin-left:0em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span><span class="mrel mtight">=</span><span class="mord mtight">1</span></span></span></span><span style="top:-3.0000050000000003em;"><span class="pstrut" style="height:3em;"></span><span><span class="mop op-symbol small-op">&#x2211;</span></span></span><span style="top:-3.950005em;margin-left:0em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">m</span></span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.9776689999999999em;"><span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord"><span class="delimsizing mult"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.173975em;"><span style="top:-1.955985em;"><span class="pstrut" style="height:2.606em;"></span><span class="delimsizinginner delim-size1"><span>&#x2223;</span></span></span><span style="top:-2.556985em;"><span class="pstrut" style="height:2.606em;"></span><span class="delimsizinginner delim-size1"><span>&#x2223;</span></span></span><span style="top:-2.572975em;"><span class="pstrut" style="height:2.606em;"></span><span class="delimsizinginner delim-size1"><span>&#x2223;</span></span></span><span style="top:-3.173975em;"><span class="pstrut" style="height:2.606em;"></span><span class="delimsizinginner delim-size1"><span>&#x2223;</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.6500149999999999em;"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.03588em;">y</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:-0.03588em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">&#x2212;</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathdefault" style="margin-right:0.10764em;">f</span><span class="mopen">(</span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mclose">)</span><span class="mord"><span class="delimsizing mult"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.173975em;"><span style="top:-1.955985em;"><span class="pstrut" style="height:2.606em;"></span><span class="delimsizinginner delim-size1"><span>&#x2223;</span></span></span><span style="top:-2.556985em;"><span class="pstrut" style="height:2.606em;"></span><span class="delimsizinginner delim-size1"><span>&#x2223;</span></span></span><span style="top:-2.572975em;"><span class="pstrut" style="height:2.606em;"></span><span class="delimsizinginner delim-size1"><span>&#x2223;</span></span></span><span style="top:-3.173975em;"><span class="pstrut" style="height:2.606em;"></span><span class="delimsizinginner delim-size1"><span>&#x2223;</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.6500149999999999em;"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></p>
<ul>
<li>&#x4F18;&#x70B9;&#x662F;&#x5176;&#x514B;&#x670D;&#x4E86;MSE&#x7684;&#x7F3A;&#x70B9;&#xFF0C;&#x53D7;&#x504F;&#x79BB;&#x6B63;&#x5E38;&#x8303;&#x56F4;&#x7684;&#x79BB;&#x7FA4;&#x6837;&#x672C;&#x5F71;&#x54CD;&#x8F83;&#x5C0F;&#x3002;</li>
<li>&#x7F3A;&#x70B9;&#x662F;&#x6536;&#x655B;&#x901F;&#x5EA6;&#x6BD4;MSE&#x6162;&#xFF0C;&#x56E0;&#x4E3A;&#x5F53;&#x8BEF;&#x5DEE;&#x5927;&#x6216;&#x5C0F;&#x65F6;&#x5176;&#x90FD;&#x4FDD;&#x6301;&#x540C;&#x7B49;&#x901F;&#x5EA6;&#x4E0B;&#x964D;&#xFF0C;&#x800C;&#x4E14;&#x5728;&#x67D0;&#x4E00;&#x70B9;&#x5904;&#x8FD8;&#x4E0D;&#x53EF;&#x5BFC;&#xFF0C;&#x8BA1;&#x7B97;&#x673A;&#x6C42;&#x5BFC;&#x6BD4;&#x8F83;&#x56F0;&#x96BE;&#x3002;</li>
</ul>
<h3 class="mume-header" id="%E5%88%86%E7%B1%BB%E9%97%AE%E9%A2%98">&#x5206;&#x7C7B;&#x95EE;&#x9898;</h3>

<h4 class="mume-header" id="cross-entropy">Cross Entropy</h4>

<p><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mrow><mi mathvariant="normal">C</mi><mi mathvariant="normal">E</mi></mrow><mo stretchy="false">(</mo><mi>p</mi><mo separator="true">,</mo><mi>q</mi><mo stretchy="false">)</mo><mo>=</mo><mo>&#x2212;</mo><munder><mo>&#x2211;</mo><mrow><mi>x</mi><mo>&#x2208;</mo><mi>X</mi></mrow></munder><mi>p</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mi>log</mi><mo>&#x2061;</mo><mi>q</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">\mathrm{CE}(p, q) = -\sum_{x&#x2208;X} p(x)\log q(x)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord"><span class="mord mathrm">C</span><span class="mord mathrm">E</span></span><span class="mopen">(</span><span class="mord mathdefault">p</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathdefault" style="margin-right:0.03588em;">q</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:2.3717110000000003em;vertical-align:-1.321706em;"></span><span class="mord">&#x2212;</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mop op-limits"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.050005em;"><span style="top:-1.8556639999999998em;margin-left:0em;"><span class="pstrut" style="height:3.05em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">x</span><span class="mrel mtight">&#x2208;</span><span class="mord mathdefault mtight" style="margin-right:0.07847em;">X</span></span></span></span><span style="top:-3.0500049999999996em;"><span class="pstrut" style="height:3.05em;"></span><span><span class="mop op-symbol large-op">&#x2211;</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:1.321706em;"><span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathdefault">p</span><span class="mopen">(</span><span class="mord mathdefault">x</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mop">lo<span style="margin-right:0.01389em;">g</span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathdefault" style="margin-right:0.03588em;">q</span><span class="mopen">(</span><span class="mord mathdefault">x</span><span class="mclose">)</span></span></span></span></span></p>
<h3 class="mume-header" id="%E9%94%99%E8%AF%AF%E7%8E%87%E4%B8%8E%E7%B2%BE%E5%BA%A6">&#x9519;&#x8BEF;&#x7387;&#x4E0E;&#x7CBE;&#x5EA6;</h3>

<p><strong>&#x9519;&#x8BEF;&#x7387;</strong></p>
<p><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>E</mi><mo>=</mo><mfrac><mrow><munderover><mo>&#x2211;</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mi>m</mi></munderover><mtext>&#x2161;</mtext><mo stretchy="false">[</mo><mi>f</mi><mo stretchy="false">(</mo><msub><mi>x</mi><mi>i</mi></msub><mo stretchy="false">)</mo><mo mathvariant="normal">&#x2260;</mo><msub><mi>y</mi><mi>i</mi></msub><mo stretchy="false">]</mo></mrow><mi>m</mi></mfrac></mrow><annotation encoding="application/x-tex">E = \dfrac{ \sum\limits_{i=1}^{m} &#x2161;[f(x_i)&#x2260;y_i] }{m}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathdefault" style="margin-right:0.05764em;">E</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:3.4050659999999997em;vertical-align:-0.686em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.7190659999999998em;"><span style="top:-2.6653970000000005em;"><span class="pstrut" style="height:3.3513970000000004em;"></span><span class="mord"><span class="mord mathdefault">m</span></span></span><span style="top:-3.5813970000000004em;"><span class="pstrut" style="height:3.3513970000000004em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-4.719066em;"><span class="pstrut" style="height:3.3513970000000004em;"></span><span class="mord"><span class="mop op-limits"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.3513970000000004em;"><span style="top:-2.122331em;margin-left:0em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span><span class="mrel mtight">=</span><span class="mord mtight">1</span></span></span></span><span style="top:-3.0000050000000003em;"><span class="pstrut" style="height:3em;"></span><span><span class="mop op-symbol small-op">&#x2211;</span></span></span><span style="top:-3.950005em;margin-left:0em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">m</span></span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.9776689999999999em;"><span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord">&#x2161;</span><span class="mopen">[</span><span class="mord mathdefault" style="margin-right:0.10764em;">f</span><span class="mopen">(</span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel"><span class="mrel"><span class="mord"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.69444em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="rlap"><span class="strut" style="height:0.8888799999999999em;vertical-align:-0.19444em;"></span><span class="inner"><span class="mrel">&#xE020;</span></span><span class="fix"></span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.19444em;"><span></span></span></span></span></span></span><span class="mrel">=</span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.03588em;">y</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:-0.03588em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mclose">]</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></p>
<p><strong>&#x7CBE;&#x5EA6;</strong></p>
<p><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>A</mi><mi>c</mi><mi>c</mi><mo>=</mo><mfrac><mrow><munderover><mo>&#x2211;</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mi>m</mi></munderover><mtext>&#x2161;</mtext><mo stretchy="false">[</mo><mi>f</mi><mo stretchy="false">(</mo><msub><mi>x</mi><mi>i</mi></msub><mo stretchy="false">)</mo><mo>=</mo><msub><mi>y</mi><mi>i</mi></msub><mo stretchy="false">]</mo></mrow><mi>m</mi></mfrac></mrow><annotation encoding="application/x-tex">Acc = \dfrac{ \sum\limits_{i=1}^{m} &#x2161;[f(x_i)=y_i] }{m}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathdefault">A</span><span class="mord mathdefault">c</span><span class="mord mathdefault">c</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:3.4050659999999997em;vertical-align:-0.686em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.7190659999999998em;"><span style="top:-2.6653970000000005em;"><span class="pstrut" style="height:3.3513970000000004em;"></span><span class="mord"><span class="mord mathdefault">m</span></span></span><span style="top:-3.5813970000000004em;"><span class="pstrut" style="height:3.3513970000000004em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-4.719066em;"><span class="pstrut" style="height:3.3513970000000004em;"></span><span class="mord"><span class="mop op-limits"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.3513970000000004em;"><span style="top:-2.122331em;margin-left:0em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span><span class="mrel mtight">=</span><span class="mord mtight">1</span></span></span></span><span style="top:-3.0000050000000003em;"><span class="pstrut" style="height:3em;"></span><span><span class="mop op-symbol small-op">&#x2211;</span></span></span><span style="top:-3.950005em;margin-left:0em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">m</span></span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.9776689999999999em;"><span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord">&#x2161;</span><span class="mopen">[</span><span class="mord mathdefault" style="margin-right:0.10764em;">f</span><span class="mopen">(</span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.03588em;">y</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:-0.03588em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mclose">]</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></p>
<h3 class="mume-header" id="%E6%B7%B7%E6%B7%86%E7%9F%A9%E9%98%B5">&#x6DF7;&#x6DC6;&#x77E9;&#x9635;</h3>

<table>
<thead>
<tr>
<th>&#x771F;&#x5B9E;&#x60C5;&#x51B5;</th>
<th>&#x9884;&#x6D4B;&#x4E3A;&#x6B63;&#x4F8B;&#xFF08;Positive&#xFF09;</th>
<th>&#x9884;&#x6D4B;&#x4E3A;&#x53CD;&#x4F8B;&#xFF08;Negatie&#xFF09;</th>
</tr>
</thead>
<tbody>
<tr>
<td>&#x6B63;&#x4F8B;&#xFF08;True&#xFF09;</td>
<td>&#x771F;&#x6B63;&#x4F8B;&#xFF08;TP&#xFF09;</td>
<td>&#x4F2A;&#x53CD;&#x4F8B;&#xFF08;FN&#xFF09;</td>
</tr>
<tr>
<td>&#x53CD;&#x4F8B;&#xFF08;False&#xFF09;</td>
<td>&#x4F2A;&#x6B63;&#x4F8B;&#xFF08;FP&#xFF09;</td>
<td>&#x771F;&#x53CD;&#x4F8B;&#xFF08;TN&#xFF09;</td>
</tr>
</tbody>
</table>
<ul>
<li><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>m</mi><mo>=</mo><mi>T</mi><mi>P</mi><mo>+</mo><mi>F</mi><mi>P</mi><mo>+</mo><mi>T</mi><mi>N</mi><mo>+</mo><mi>F</mi><mi>N</mi></mrow><annotation encoding="application/x-tex">m = TP + FP + TN + FN</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em;"></span><span class="mord mathdefault">m</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.76666em;vertical-align:-0.08333em;"></span><span class="mord mathdefault" style="margin-right:0.13889em;">T</span><span class="mord mathdefault" style="margin-right:0.13889em;">P</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:0.76666em;vertical-align:-0.08333em;"></span><span class="mord mathdefault" style="margin-right:0.13889em;">F</span><span class="mord mathdefault" style="margin-right:0.13889em;">P</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:0.76666em;vertical-align:-0.08333em;"></span><span class="mord mathdefault" style="margin-right:0.13889em;">T</span><span class="mord mathdefault" style="margin-right:0.10903em;">N</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathdefault" style="margin-right:0.13889em;">F</span><span class="mord mathdefault" style="margin-right:0.10903em;">N</span></span></span></span></li>
</ul>
<h4 class="mume-header" id="%E5%87%86%E7%A1%AE%E7%8E%87">&#x51C6;&#x786E;&#x7387;</h4>

<p><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>A</mi><mi>c</mi><mi>c</mi><mi>u</mi><mi>r</mi><mi>a</mi><mi>c</mi><mi>y</mi><mo>=</mo><mfrac><mrow><mi>T</mi><mi>P</mi><mo>+</mo><mi>T</mi><mi>N</mi></mrow><mi>m</mi></mfrac><mo>=</mo><mfrac><mrow><mi>T</mi><mi>P</mi><mo>+</mo><mi>T</mi><mi>N</mi></mrow><mrow><mi>T</mi><mi>P</mi><mo>+</mo><mi>F</mi><mi>P</mi><mo>+</mo><mi>T</mi><mi>N</mi><mo>+</mo><mi>F</mi><mi>N</mi></mrow></mfrac></mrow><annotation encoding="application/x-tex">Accuracy = \dfrac{TP+TN}{m} = \dfrac{TP+TN}{TP + FP + TN + FN}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8777699999999999em;vertical-align:-0.19444em;"></span><span class="mord mathdefault">A</span><span class="mord mathdefault">c</span><span class="mord mathdefault">c</span><span class="mord mathdefault">u</span><span class="mord mathdefault" style="margin-right:0.02778em;">r</span><span class="mord mathdefault">a</span><span class="mord mathdefault">c</span><span class="mord mathdefault" style="margin-right:0.03588em;">y</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:2.04633em;vertical-align:-0.686em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.36033em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault">m</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em;">T</span><span class="mord mathdefault" style="margin-right:0.13889em;">P</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathdefault" style="margin-right:0.13889em;">T</span><span class="mord mathdefault" style="margin-right:0.10903em;">N</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:2.1296600000000003em;vertical-align:-0.7693300000000001em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.36033em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em;">T</span><span class="mord mathdefault" style="margin-right:0.13889em;">P</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathdefault" style="margin-right:0.13889em;">F</span><span class="mord mathdefault" style="margin-right:0.13889em;">P</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathdefault" style="margin-right:0.13889em;">T</span><span class="mord mathdefault" style="margin-right:0.10903em;">N</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathdefault" style="margin-right:0.13889em;">F</span><span class="mord mathdefault" style="margin-right:0.10903em;">N</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em;">T</span><span class="mord mathdefault" style="margin-right:0.13889em;">P</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathdefault" style="margin-right:0.13889em;">T</span><span class="mord mathdefault" style="margin-right:0.10903em;">N</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.7693300000000001em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></p>
<h4 class="mume-header" id="%E7%89%B9%E5%BC%82%E5%BA%A6">&#x7279;&#x5F02;&#x5EA6;</h4>

<p><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>S</mi><mi>p</mi><mi>e</mi><mi>c</mi><mi>i</mi><mi>f</mi><mi>i</mi><mi>c</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo>=</mo><mfrac><mrow><mi>T</mi><mi>N</mi></mrow><mrow><mi>F</mi><mi>a</mi><mi>l</mi><mi>s</mi><mi>e</mi></mrow></mfrac><mo>=</mo><mfrac><mrow><mi>T</mi><mi>N</mi></mrow><mrow><mi>F</mi><mi>P</mi><mo>+</mo><mi>T</mi><mi>N</mi></mrow></mfrac></mrow><annotation encoding="application/x-tex">Specificity = \dfrac{TN}{False} = \dfrac{TN}{FP + TN}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8888799999999999em;vertical-align:-0.19444em;"></span><span class="mord mathdefault" style="margin-right:0.05764em;">S</span><span class="mord mathdefault">p</span><span class="mord mathdefault">e</span><span class="mord mathdefault">c</span><span class="mord mathdefault">i</span><span class="mord mathdefault" style="margin-right:0.10764em;">f</span><span class="mord mathdefault">i</span><span class="mord mathdefault">c</span><span class="mord mathdefault">i</span><span class="mord mathdefault">t</span><span class="mord mathdefault" style="margin-right:0.03588em;">y</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:2.04633em;vertical-align:-0.686em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.36033em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em;">F</span><span class="mord mathdefault">a</span><span class="mord mathdefault" style="margin-right:0.01968em;">l</span><span class="mord mathdefault">s</span><span class="mord mathdefault">e</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em;">T</span><span class="mord mathdefault" style="margin-right:0.10903em;">N</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:2.1296600000000003em;vertical-align:-0.7693300000000001em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.36033em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em;">F</span><span class="mord mathdefault" style="margin-right:0.13889em;">P</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathdefault" style="margin-right:0.13889em;">T</span><span class="mord mathdefault" style="margin-right:0.10903em;">N</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em;">T</span><span class="mord mathdefault" style="margin-right:0.10903em;">N</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.7693300000000001em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></p>
<h4 class="mume-header" id="%E7%B2%BE%E7%A1%AE%E7%8E%87%E6%9F%A5%E5%87%86%E7%8E%87">&#x7CBE;&#x786E;&#x7387;&#xFF08;&#x67E5;&#x51C6;&#x7387;&#xFF09;</h4>

<p><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>P</mi><mi>r</mi><mi>e</mi><mi>c</mi><mi>i</mi><mi>s</mi><mi>i</mi><mi>o</mi><mi>n</mi><mo>=</mo><mfrac><mrow><mi>T</mi><mi>P</mi></mrow><mrow><mi>P</mi><mi>o</mi><mi>s</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>e</mi></mrow></mfrac><mo>=</mo><mfrac><mrow><mi>T</mi><mi>P</mi></mrow><mrow><mi>T</mi><mi>P</mi><mo>+</mo><mi>F</mi><mi>P</mi></mrow></mfrac></mrow><annotation encoding="application/x-tex">Precision = \dfrac{TP}{Positive} = \dfrac{TP}{TP + FP}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathdefault" style="margin-right:0.13889em;">P</span><span class="mord mathdefault" style="margin-right:0.02778em;">r</span><span class="mord mathdefault">e</span><span class="mord mathdefault">c</span><span class="mord mathdefault">i</span><span class="mord mathdefault">s</span><span class="mord mathdefault">i</span><span class="mord mathdefault">o</span><span class="mord mathdefault">n</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:2.04633em;vertical-align:-0.686em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.36033em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em;">P</span><span class="mord mathdefault">o</span><span class="mord mathdefault">s</span><span class="mord mathdefault">i</span><span class="mord mathdefault">t</span><span class="mord mathdefault">i</span><span class="mord mathdefault" style="margin-right:0.03588em;">v</span><span class="mord mathdefault">e</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em;">T</span><span class="mord mathdefault" style="margin-right:0.13889em;">P</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:2.1296600000000003em;vertical-align:-0.7693300000000001em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.36033em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em;">T</span><span class="mord mathdefault" style="margin-right:0.13889em;">P</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathdefault" style="margin-right:0.13889em;">F</span><span class="mord mathdefault" style="margin-right:0.13889em;">P</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em;">T</span><span class="mord mathdefault" style="margin-right:0.13889em;">P</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.7693300000000001em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></p>
<h4 class="mume-header" id="%E5%8F%AC%E5%9B%9E%E7%8E%87%E6%9F%A5%E5%85%A8%E7%8E%87">&#x53EC;&#x56DE;&#x7387;&#xFF08;&#x67E5;&#x5168;&#x7387;&#xFF09;</h4>

<p><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>R</mi><mi>e</mi><mi>c</mi><mi>a</mi><mi>l</mi><mi>l</mi><mo>=</mo><mfrac><mrow><mi>T</mi><mi>P</mi></mrow><mrow><mi>T</mi><mi>r</mi><mi>u</mi><mi>e</mi></mrow></mfrac><mo>=</mo><mfrac><mrow><mi>T</mi><mi>P</mi></mrow><mrow><mi>T</mi><mi>P</mi><mo>+</mo><mi>F</mi><mi>N</mi></mrow></mfrac></mrow><annotation encoding="application/x-tex">Recall = \dfrac{TP}{True} = \dfrac{TP}{TP + FN}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.69444em;vertical-align:0em;"></span><span class="mord mathdefault" style="margin-right:0.00773em;">R</span><span class="mord mathdefault">e</span><span class="mord mathdefault">c</span><span class="mord mathdefault">a</span><span class="mord mathdefault" style="margin-right:0.01968em;">l</span><span class="mord mathdefault" style="margin-right:0.01968em;">l</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:2.04633em;vertical-align:-0.686em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.36033em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em;">T</span><span class="mord mathdefault" style="margin-right:0.02778em;">r</span><span class="mord mathdefault">u</span><span class="mord mathdefault">e</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em;">T</span><span class="mord mathdefault" style="margin-right:0.13889em;">P</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:2.1296600000000003em;vertical-align:-0.7693300000000001em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.36033em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em;">T</span><span class="mord mathdefault" style="margin-right:0.13889em;">P</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathdefault" style="margin-right:0.13889em;">F</span><span class="mord mathdefault" style="margin-right:0.10903em;">N</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em;">T</span><span class="mord mathdefault" style="margin-right:0.13889em;">P</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.7693300000000001em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></p>
<h4 class="mume-header" id="%E5%B9%B3%E8%A1%A1%E7%82%B9bepbreak-even-point">&#x5E73;&#x8861;&#x70B9;&#xFF08;BEP&#xFF0C;Break-Even Point&#xFF09;</h4>

<p>&#x67E5;&#x51C6;&#x7387;&#x548C;&#x67E5;&#x5168;&#x7387;&#x662F;&#x4E00;&#x5BF9;&#x77DB;&#x76FE;&#x7684;&#x53D8;&#x91CF;&#xFF0C;&#x5E73;&#x8861;&#x70B9;&#x5C31;&#x662F;&#x67E5;&#x51C6;&#x7387;&#x7B49;&#x4E8E;&#x67E5;&#x5168;&#x7387;&#x65F6;&#x7684;&#x53D6;&#x503C;&#x3002;<br>
<img src="./images/e_BEP.png" alt></p>
<h4 class="mume-header" id="f_1"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>F</mi><mn>1</mn></msub></mrow><annotation encoding="application/x-tex">F_1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em;">F</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:-0.13889em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span></h4>

<p><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mtable rowspacing="0.15999999999999992em" columnalign="right" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><msub><mi>F</mi><mn>1</mn></msub></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow></mrow></mstyle></mtd></mtr></mtable><mtable rowspacing="0.15999999999999992em" columnalign="left" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mo>=</mo><mstyle displaystyle="true" scriptlevel="0"><mfrac><mn>1</mn><mrow><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>&#x22C5;</mo><mfrac><mn>1</mn><mrow><mi>P</mi><mi>r</mi><mi>e</mi><mi>c</mi><mi>i</mi><mi>s</mi><mi>i</mi><mi>o</mi><mi>n</mi></mrow></mfrac><mo>+</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>&#x22C5;</mo><mfrac><mn>1</mn><mrow><mi>R</mi><mi>e</mi><mi>c</mi><mi>a</mi><mi>l</mi><mi>l</mi></mrow></mfrac></mrow></mfrac></mstyle></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mo>=</mo><mstyle displaystyle="true" scriptlevel="0"><mfrac><mrow><mn>2</mn><mo>&#x22C5;</mo><mi>P</mi><mi>r</mi><mi>e</mi><mi>c</mi><mi>i</mi><mi>s</mi><mi>i</mi><mi>o</mi><mi>n</mi><mo>&#x22C5;</mo><mi>R</mi><mi>e</mi><mi>c</mi><mi>a</mi><mi>l</mi><mi>l</mi></mrow><mrow><mi>P</mi><mi>r</mi><mi>e</mi><mi>c</mi><mi>i</mi><mi>s</mi><mi>i</mi><mi>o</mi><mi>n</mi><mo>+</mo><mi>R</mi><mi>e</mi><mi>c</mi><mi>a</mi><mi>l</mi><mi>l</mi></mrow></mfrac></mstyle></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mo>=</mo><mstyle displaystyle="true" scriptlevel="0"><mfrac><mrow><mn>2</mn><mi>T</mi><mi>P</mi></mrow><mrow><mn>2</mn><mi>T</mi><mi>P</mi><mo>+</mo><mi>F</mi><mi>N</mi><mo>+</mo><mi>F</mi><mi>P</mi></mrow></mfrac></mstyle></mrow></mstyle></mtd></mtr></mtable></mrow><annotation encoding="application/x-tex">\begin{array}{r}
    F_1
\\ \\ \\ \\ \\ \\ \\
\end{array} \begin{array}{l}
    = \dfrac{1}{
        \frac{1}{2} &#x22C5; \frac{1}{Precision} +
        \frac{1}{2} &#x22C5; \frac{1}{Recall}
    }
\\
\\  = \dfrac{2 &#x22C5; Precision&#x22C5;Recall}{Precision + Recall}
\\
\\  = \dfrac{2TP}{2TP + FN + FP}
\end{array}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:9.071978em;vertical-align:-4.285989em;"></span><span class="mord"><span class="mtable"><span class="arraycolsep" style="width:0.5em;"></span><span class="col-align-r"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:4.450000000000001em;"><span style="top:-6.61em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em;">F</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:-0.13889em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span><span style="top:-5.410000000000001em;"><span class="pstrut" style="height:3em;"></span><span class="mord"></span></span><span style="top:-4.210000000000001em;"><span class="pstrut" style="height:3em;"></span><span class="mord"></span></span><span style="top:-3.0100000000000002em;"><span class="pstrut" style="height:3em;"></span><span class="mord"></span></span><span style="top:-1.8100000000000003em;"><span class="pstrut" style="height:3em;"></span><span class="mord"></span></span><span style="top:-0.6100000000000001em;"><span class="pstrut" style="height:3em;"></span><span class="mord"></span></span><span style="top:0.5900000000000001em;"><span class="pstrut" style="height:3em;"></span><span class="mord"></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:3.95em;"><span></span></span></span></span></span><span class="arraycolsep" style="width:0.5em;"></span></span></span><span class="mord"><span class="mtable"><span class="arraycolsep" style="width:0.5em;"></span><span class="col-align-l"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:4.785989em;"><span style="top:-6.835989em;"><span class="pstrut" style="height:3.3714399999999998em;"></span><span class="mord"><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.32144em;"><span style="top:-2.2648919999999997em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.845108em;"><span style="top:-2.6550000000000002em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">2</span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.394em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">&#x22C5;</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.845108em;"><span style="top:-2.6550000000000002em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.13889em;">P</span><span class="mord mathdefault mtight" style="margin-right:0.02778em;">r</span><span class="mord mathdefault mtight">e</span><span class="mord mathdefault mtight">c</span><span class="mord mathdefault mtight">i</span><span class="mord mathdefault mtight">s</span><span class="mord mathdefault mtight">i</span><span class="mord mathdefault mtight">o</span><span class="mord mathdefault mtight">n</span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.394em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.845108em;"><span style="top:-2.6550000000000002em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">2</span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.394em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">&#x22C5;</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.845108em;"><span style="top:-2.6550000000000002em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.00773em;">R</span><span class="mord mathdefault mtight">e</span><span class="mord mathdefault mtight">c</span><span class="mord mathdefault mtight">a</span><span class="mord mathdefault mtight" style="margin-right:0.01968em;">l</span><span class="mord mathdefault mtight" style="margin-right:0.01968em;">l</span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.394em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">1</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:1.080108em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span><span style="top:-4.915881em;"><span class="pstrut" style="height:3.3714399999999998em;"></span><span class="mord"></span></span><span style="top:-3.1844409999999996em;"><span class="pstrut" style="height:3.3714399999999998em;"></span><span class="mord"><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.37144em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em;">P</span><span class="mord mathdefault" style="margin-right:0.02778em;">r</span><span class="mord mathdefault">e</span><span class="mord mathdefault">c</span><span class="mord mathdefault">i</span><span class="mord mathdefault">s</span><span class="mord mathdefault">i</span><span class="mord mathdefault">o</span><span class="mord mathdefault">n</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathdefault" style="margin-right:0.00773em;">R</span><span class="mord mathdefault">e</span><span class="mord mathdefault">c</span><span class="mord mathdefault">a</span><span class="mord mathdefault" style="margin-right:0.01968em;">l</span><span class="mord mathdefault" style="margin-right:0.01968em;">l</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">2</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">&#x22C5;</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathdefault" style="margin-right:0.13889em;">P</span><span class="mord mathdefault" style="margin-right:0.02778em;">r</span><span class="mord mathdefault">e</span><span class="mord mathdefault">c</span><span class="mord mathdefault">i</span><span class="mord mathdefault">s</span><span class="mord mathdefault">i</span><span class="mord mathdefault">o</span><span class="mord mathdefault">n</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">&#x22C5;</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathdefault" style="margin-right:0.00773em;">R</span><span class="mord mathdefault">e</span><span class="mord mathdefault">c</span><span class="mord mathdefault">a</span><span class="mord mathdefault" style="margin-right:0.01968em;">l</span><span class="mord mathdefault" style="margin-right:0.01968em;">l</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.7693300000000001em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span><span style="top:-1.5751109999999995em;"><span class="pstrut" style="height:3.3714399999999998em;"></span><span class="mord"></span></span><span style="top:0.145219em;"><span class="pstrut" style="height:3.3714399999999998em;"></span><span class="mord"><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.36033em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">2</span><span class="mord mathdefault" style="margin-right:0.13889em;">T</span><span class="mord mathdefault" style="margin-right:0.13889em;">P</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathdefault" style="margin-right:0.13889em;">F</span><span class="mord mathdefault" style="margin-right:0.10903em;">N</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathdefault" style="margin-right:0.13889em;">F</span><span class="mord mathdefault" style="margin-right:0.13889em;">P</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">2</span><span class="mord mathdefault" style="margin-right:0.13889em;">T</span><span class="mord mathdefault" style="margin-right:0.13889em;">P</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.7693300000000001em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:4.285989em;"><span></span></span></span></span></span><span class="arraycolsep" style="width:0.5em;"></span></span></span></span></span></span></span></p>
<p><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>F</mi><mn>1</mn></mrow><annotation encoding="application/x-tex">F1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathdefault" style="margin-right:0.13889em;">F</span><span class="mord">1</span></span></span></span>&#x662F;&#x57FA;&#x4E8E;&#x67E5;&#x51C6;&#x7387;&#x548C;&#x67E5;&#x5168;&#x7387;&#x7684;&#x8C03;&#x548C;&#x5E73;&#x5747;&#x6570;&#x3002;</p>
<h4 class="mume-header" id="f_%CE%B2"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>F</mi><mi>&#x3B2;</mi></msub></mrow><annotation encoding="application/x-tex">F_&#x3B2;</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.969438em;vertical-align:-0.286108em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em;">F</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361079999999999em;"><span style="top:-2.5500000000000003em;margin-left:-0.13889em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.05278em;">&#x3B2;</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em;"><span></span></span></span></span></span></span></span></span></span></h4>

<p><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mtable rowspacing="0.15999999999999992em" columnalign="right" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><msub><mi>F</mi><mi>&#x3B2;</mi></msub></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow></mrow></mstyle></mtd></mtr></mtable><mtable rowspacing="0.15999999999999992em" columnalign="left" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mo>=</mo><mstyle displaystyle="true" scriptlevel="0"><mfrac><mn>1</mn><mrow><mfrac><mn>1</mn><mrow><msup><mi>&#x3B2;</mi><mn>2</mn></msup><mo>+</mo><mn>1</mn></mrow></mfrac><mo>&#x22C5;</mo><mfrac><mn>1</mn><mrow><mi>P</mi><mi>r</mi><mi>e</mi><mi>c</mi><mi>i</mi><mi>s</mi><mi>i</mi><mi>o</mi><mi>n</mi></mrow></mfrac><mo>+</mo><mfrac><msup><mi>&#x3B2;</mi><mn>2</mn></msup><mrow><msup><mi>&#x3B2;</mi><mn>2</mn></msup><mo>+</mo><mn>1</mn></mrow></mfrac><mo>&#x22C5;</mo><mfrac><mn>1</mn><mrow><mi>R</mi><mi>e</mi><mi>c</mi><mi>a</mi><mi>l</mi><mi>l</mi></mrow></mfrac></mrow></mfrac></mstyle></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mo>=</mo><mstyle displaystyle="true" scriptlevel="0"><mfrac><mrow><mo stretchy="false">(</mo><mn>1</mn><mo>+</mo><msup><mi>&#x3B2;</mi><mn>2</mn></msup><mo stretchy="false">)</mo><mo>&#x22C5;</mo><mi>P</mi><mi>r</mi><mi>e</mi><mi>c</mi><mi>i</mi><mi>s</mi><mi>i</mi><mi>o</mi><mi>n</mi><mo>&#x22C5;</mo><mi>R</mi><mi>e</mi><mi>c</mi><mi>a</mi><mi>l</mi><mi>l</mi></mrow><mrow><msup><mi>&#x3B2;</mi><mn>2</mn></msup><mo>&#x22C5;</mo><mi>P</mi><mi>r</mi><mi>e</mi><mi>c</mi><mi>i</mi><mi>s</mi><mi>i</mi><mi>o</mi><mi>n</mi><mo>+</mo><mi>R</mi><mi>e</mi><mi>c</mi><mi>a</mi><mi>l</mi><mi>l</mi></mrow></mfrac></mstyle></mrow></mstyle></mtd></mtr></mtable></mrow><annotation encoding="application/x-tex">\begin{array}{r}
    F_&#x3B2;
\\ \\ \\ \\ \\
\end{array} \begin{array}{l}
    = \dfrac{1}{
        \frac{1}{&#x3B2;^2+1} &#x22C5; \frac{1}{Precision} +
        \frac{&#x3B2;^2}{&#x3B2;^2+1} &#x22C5; \frac{1}{Recall}
    }
\\
\\  = \dfrac{ (1+&#x3B2;^2) &#x22C5; Precision &#x22C5; Recall }{ &#x3B2;^2 &#x22C5; Precision + Recall }
\end{array}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:6.232624em;vertical-align:-2.866312em;"></span><span class="mord"><span class="mtable"><span class="arraycolsep" style="width:0.5em;"></span><span class="col-align-r"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:3.2500000000000004em;"><span style="top:-5.410000000000001em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em;">F</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361079999999999em;"><span style="top:-2.5500000000000003em;margin-left:-0.13889em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.05278em;">&#x3B2;</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em;"><span></span></span></span></span></span></span></span></span><span style="top:-4.21em;"><span class="pstrut" style="height:3em;"></span><span class="mord"></span></span><span style="top:-3.01em;"><span class="pstrut" style="height:3em;"></span><span class="mord"></span></span><span style="top:-1.8099999999999998em;"><span class="pstrut" style="height:3em;"></span><span class="mord"></span></span><span style="top:-0.6099999999999997em;"><span class="pstrut" style="height:3em;"></span><span class="mord"></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:2.7500000000000004em;"><span></span></span></span></span></span><span class="arraycolsep" style="width:0.5em;"></span></span></span><span class="mord"><span class="mtable"><span class="arraycolsep" style="width:0.5em;"></span><span class="col-align-l"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:3.366312em;"><span style="top:-5.53598em;"><span class="pstrut" style="height:3.491108em;"></span><span class="mord"><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.32144em;"><span style="top:-2.141472em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.845108em;"><span style="top:-2.6550000000000002em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.05278em;">&#x3B2;</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.7463142857142857em;"><span style="top:-2.786em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span><span class="mbin mtight">+</span><span class="mord mtight">1</span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.394em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.481108em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">&#x22C5;</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.845108em;"><span style="top:-2.6550000000000002em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.13889em;">P</span><span class="mord mathdefault mtight" style="margin-right:0.02778em;">r</span><span class="mord mathdefault mtight">e</span><span class="mord mathdefault mtight">c</span><span class="mord mathdefault mtight">i</span><span class="mord mathdefault mtight">s</span><span class="mord mathdefault mtight">i</span><span class="mord mathdefault mtight">o</span><span class="mord mathdefault mtight">n</span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.394em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.9685280000000001em;"><span style="top:-2.6550000000000002em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.05278em;">&#x3B2;</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.7463142857142857em;"><span style="top:-2.786em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span><span class="mbin mtight">+</span><span class="mord mtight">1</span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.446108em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.05278em;">&#x3B2;</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.7463142857142857em;"><span style="top:-2.786em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.481108em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">&#x22C5;</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.845108em;"><span style="top:-2.6550000000000002em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.00773em;">R</span><span class="mord mathdefault mtight">e</span><span class="mord mathdefault mtight">c</span><span class="mord mathdefault mtight">a</span><span class="mord mathdefault mtight" style="margin-right:0.01968em;">l</span><span class="mord mathdefault mtight" style="margin-right:0.01968em;">l</span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.394em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">1</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:1.339636em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span><span style="top:-3.3563439999999995em;"><span class="pstrut" style="height:3.491108em;"></span><span class="mord"></span></span><span style="top:-1.505236em;"><span class="pstrut" style="height:3.491108em;"></span><span class="mord"><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.491108em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"><span class="mord mathdefault" style="margin-right:0.05278em;">&#x3B2;</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.740108em;"><span style="top:-2.9890000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">&#x22C5;</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathdefault" style="margin-right:0.13889em;">P</span><span class="mord mathdefault" style="margin-right:0.02778em;">r</span><span class="mord mathdefault">e</span><span class="mord mathdefault">c</span><span class="mord mathdefault">i</span><span class="mord mathdefault">s</span><span class="mord mathdefault">i</span><span class="mord mathdefault">o</span><span class="mord mathdefault">n</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathdefault" style="margin-right:0.00773em;">R</span><span class="mord mathdefault">e</span><span class="mord mathdefault">c</span><span class="mord mathdefault">a</span><span class="mord mathdefault" style="margin-right:0.01968em;">l</span><span class="mord mathdefault" style="margin-right:0.01968em;">l</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mopen">(</span><span class="mord">1</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.05278em;">&#x3B2;</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141079999999999em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">&#x22C5;</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathdefault" style="margin-right:0.13889em;">P</span><span class="mord mathdefault" style="margin-right:0.02778em;">r</span><span class="mord mathdefault">e</span><span class="mord mathdefault">c</span><span class="mord mathdefault">i</span><span class="mord mathdefault">s</span><span class="mord mathdefault">i</span><span class="mord mathdefault">o</span><span class="mord mathdefault">n</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">&#x22C5;</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathdefault" style="margin-right:0.00773em;">R</span><span class="mord mathdefault">e</span><span class="mord mathdefault">c</span><span class="mord mathdefault">a</span><span class="mord mathdefault" style="margin-right:0.01968em;">l</span><span class="mord mathdefault" style="margin-right:0.01968em;">l</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.8804400000000001em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:2.866312em;"><span></span></span></span></span></span><span class="arraycolsep" style="width:0.5em;"></span></span></span></span></span></span></span></p>
<p><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>F</mi><mi>&#x3B2;</mi></msub></mrow><annotation encoding="application/x-tex">F_&#x3B2;</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.969438em;vertical-align:-0.286108em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em;">F</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361079999999999em;"><span style="top:-2.5500000000000003em;margin-left:-0.13889em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.05278em;">&#x3B2;</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em;"><span></span></span></span></span></span></span></span></span></span>&#x662F;&#x57FA;&#x4E8E;&#x67E5;&#x51C6;&#x7387;&#x548C;&#x67E5;&#x5168;&#x7387;&#x7684;&#x52A0;&#x6743;&#x8C03;&#x548C;&#x5E73;&#x5747;&#x6570;&#xFF0C;&#x5F53;<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>&#x3B2;</mi><mo>=</mo><mn>1</mn></mrow><annotation encoding="application/x-tex">&#x3B2;=1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8888799999999999em;vertical-align:-0.19444em;"></span><span class="mord mathdefault" style="margin-right:0.05278em;">&#x3B2;</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord">1</span></span></span></span>&#x65F6;&#xFF0C;&#x5373;&#x4E3A;<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>F</mi><mn>1</mn></msub></mrow><annotation encoding="application/x-tex">F_1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em;">F</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:-0.13889em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span>&#x3002;</p>
<h4 class="mume-header" id="roc">ROC</h4>

<p>ROC&#xFF08;Receiver Operating Characteristic&#xFF0C;&#x53D7;&#x8BD5;&#x8005;&#x5DE5;&#x4F5C;&#x7279;&#x5F81;&#xFF09;&#x66F2;&#x7EBF;&#x7EB5;&#x8F74;&#x4E3A;&#x201C;<strong>&#x771F;&#x6B63;&#x4F8B;&#x7387;&#xFF08;TPR&#xFF0C;True Positive Rate&#xFF09;</strong>&#x201D;&#xFF0C;&#x6A2A;&#x8F74;&#x662F;&#x201C;<strong>&#x5047;&#x6B63;&#x4F8B;&#x7387;&#xFF08;FPR&#xFF0C;False Positive Rate&#xFF09;</strong>&#x201D;&#x3002;</p>
<ul>
<li><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>T</mi><mi>P</mi><mi>R</mi><mo>=</mo><mstyle displaystyle="true" scriptlevel="0"><mfrac><mrow><mi>T</mi><mi>P</mi></mrow><mrow><mi>T</mi><mi>r</mi><mi>u</mi><mi>e</mi></mrow></mfrac></mstyle><mo>=</mo><mstyle displaystyle="true" scriptlevel="0"><mfrac><mrow><mi>T</mi><mi>P</mi></mrow><mrow><mi>T</mi><mi>P</mi><mo>+</mo><mi>F</mi><mi>N</mi></mrow></mfrac></mstyle></mrow><annotation encoding="application/x-tex">TPR = \dfrac{TP}{True} = \dfrac{TP}{TP + FN}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathdefault" style="margin-right:0.13889em;">T</span><span class="mord mathdefault" style="margin-right:0.13889em;">P</span><span class="mord mathdefault" style="margin-right:0.00773em;">R</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:2.04633em;vertical-align:-0.686em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.36033em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em;">T</span><span class="mord mathdefault" style="margin-right:0.02778em;">r</span><span class="mord mathdefault">u</span><span class="mord mathdefault">e</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em;">T</span><span class="mord mathdefault" style="margin-right:0.13889em;">P</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:2.1296600000000003em;vertical-align:-0.7693300000000001em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.36033em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em;">T</span><span class="mord mathdefault" style="margin-right:0.13889em;">P</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathdefault" style="margin-right:0.13889em;">F</span><span class="mord mathdefault" style="margin-right:0.10903em;">N</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em;">T</span><span class="mord mathdefault" style="margin-right:0.13889em;">P</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.7693300000000001em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></li>
<li><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>F</mi><mi>P</mi><mi>R</mi><mo>=</mo><mstyle displaystyle="true" scriptlevel="0"><mfrac><mrow><mi>F</mi><mi>P</mi></mrow><mrow><mi>F</mi><mi>a</mi><mi>l</mi><mi>s</mi><mi>e</mi></mrow></mfrac></mstyle><mo>=</mo><mstyle displaystyle="true" scriptlevel="0"><mfrac><mrow><mi>F</mi><mi>P</mi></mrow><mrow><mi>F</mi><mi>P</mi><mo>+</mo><mi>T</mi><mi>N</mi></mrow></mfrac></mstyle></mrow><annotation encoding="application/x-tex">FPR = \dfrac{FP}{False} = \dfrac{FP}{FP + TN}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathdefault" style="margin-right:0.13889em;">F</span><span class="mord mathdefault" style="margin-right:0.13889em;">P</span><span class="mord mathdefault" style="margin-right:0.00773em;">R</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:2.04633em;vertical-align:-0.686em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.36033em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em;">F</span><span class="mord mathdefault">a</span><span class="mord mathdefault" style="margin-right:0.01968em;">l</span><span class="mord mathdefault">s</span><span class="mord mathdefault">e</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em;">F</span><span class="mord mathdefault" style="margin-right:0.13889em;">P</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:2.1296600000000003em;vertical-align:-0.7693300000000001em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.36033em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em;">F</span><span class="mord mathdefault" style="margin-right:0.13889em;">P</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathdefault" style="margin-right:0.13889em;">T</span><span class="mord mathdefault" style="margin-right:0.10903em;">N</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em;">F</span><span class="mord mathdefault" style="margin-right:0.13889em;">P</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.7693300000000001em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></li>
</ul>
<p><img src="./images/e_ROC_AUC.png" alt></p>
<p>&#x201C;<strong>AUC&#xFF08;Area Under Curve&#xFF09;</strong>&#x201D;&#x4E3A;ROC&#x66F2;&#x7EBF;&#x6240;&#x8986;&#x76D6;&#x7684;&#x533A;&#x57DF;&#x9762;&#x79EF;&#x3002;AUC&#x8D8A;&#x5927;&#xFF0C;&#x5206;&#x7C7B;&#x5668;&#x5206;&#x7C7B;&#x6548;&#x679C;&#x8D8A;&#x597D;&#x3002;</p>
<table>
<thead>
<tr>
<th>AUC</th>
<th>&#x6548;&#x679C;</th>
</tr>
</thead>
<tbody>
<tr>
<td><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>1</mn></mrow><annotation encoding="application/x-tex">1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord">1</span></span></span></span></td>
<td>&#x5B8C;&#x7F8E;&#x5206;&#x7C7B;&#x5668;</td>
</tr>
<tr>
<td><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">(</mo><mn>0.5</mn><mo separator="true">,</mo><mn>1</mn><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">(0.5,1)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord">0</span><span class="mord">.</span><span class="mord">5</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord">1</span><span class="mclose">)</span></span></span></span></td>
<td>&#x4F18;&#x4E8E;&#x968F;&#x673A;&#x731C;&#x6D4B;</td>
</tr>
<tr>
<td><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>0.5</mn></mrow><annotation encoding="application/x-tex">0.5</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord">0</span><span class="mord">.</span><span class="mord">5</span></span></span></span></td>
<td>&#x7B49;&#x4EF7;&#x4E8E;&#x968F;&#x673A;&#x731C;&#x6D4B;</td>
</tr>
<tr>
<td><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">(</mo><mn>0</mn><mo separator="true">,</mo><mn>0.5</mn><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">(0,0.5)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord">0</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord">0</span><span class="mord">.</span><span class="mord">5</span><span class="mclose">)</span></span></span></span></td>
<td>&#x5DEE;&#x4E8E;&#x968F;&#x673A;&#x731C;&#x6D4B;</td>
</tr>
</tbody>
</table>
<h2 class="mume-header" id="%E4%BB%A3%E4%BB%B7">&#x4EE3;&#x4EF7;</h2>

<p>&#x5728;&#x975E;&#x5747;&#x7B49;&#x4EE3;&#x4EF7;&#x4E0B;ROC&#x66F2;&#x7EBF;&#x4E0D;&#x80FD;&#x53CD;&#x6620;&#x51FA;&#x5B66;&#x4E60;&#x5668;&#x7684;&#x671F;&#x671B;&#x603B;&#x4F53;&#x4EE3;&#x4EF7;&#x3002;</p>
<p><img src="./images/e_cost2.png" alt></p>
<h3 class="mume-header" id="%E4%BB%A3%E4%BB%B7%E6%95%8F%E6%84%9Fcost-sensitive%E9%94%99%E8%AF%AF%E7%8E%87">&#x4EE3;&#x4EF7;&#x654F;&#x611F;&#xFF08;Cost-Sensitive&#xFF09;&#x9519;&#x8BEF;&#x7387;</h3>

<p><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>E</mi><mo>=</mo><mfrac><mrow><munder><mo>&#x2211;</mo><mrow><msub><mi>x</mi><mi>i</mi></msub><mo>&#x2208;</mo><msup><mi>D</mi><mo>+</mo></msup></mrow></munder><mtext>&#x2161;</mtext><mo stretchy="false">(</mo><mi>f</mi><mo stretchy="false">(</mo><msub><mi>x</mi><mi>i</mi></msub><mo stretchy="false">)</mo><mo mathvariant="normal">&#x2260;</mo><msub><mi>y</mi><mi>i</mi></msub><mo stretchy="false">)</mo><mi>c</mi><mi>o</mi><mi>s</mi><msub><mi>t</mi><mn>01</mn></msub><mo>+</mo><munder><mo>&#x2211;</mo><mrow><msub><mi>x</mi><mi>i</mi></msub><mo>&#x2208;</mo><msup><mi>D</mi><mo>&#x2212;</mo></msup></mrow></munder><mtext>&#x2161;</mtext><mo stretchy="false">(</mo><mi>f</mi><mo stretchy="false">(</mo><msub><mi>x</mi><mi>i</mi></msub><mo stretchy="false">)</mo><mo mathvariant="normal">&#x2260;</mo><msub><mi>y</mi><mi>i</mi></msub><mo stretchy="false">)</mo><mi>c</mi><mi>o</mi><mi>s</mi><msub><mi>t</mi><mn>10</mn></msub></mrow><mi>m</mi></mfrac></mrow><annotation encoding="application/x-tex">E = \dfrac{
    \sum\limits_{x_i&#x2208;D^+} &#x2161;(f(x_i)&#x2260;y_i) cost_{01} +
    \sum\limits_{x_i&#x2208;D^-} &#x2161;(f(x_i)&#x2260;y_i) cost_{10}
}{m}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathdefault" style="margin-right:0.05764em;">E</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:2.933975em;vertical-align:-0.686em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.2479750000000003em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault">m</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-4.4979700000000005em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mop op-limits"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.7500050000000003em;"><span style="top:-2.09213em;margin-left:0em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathdefault mtight">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3280857142857143em;"><span style="top:-2.357em;margin-left:0em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mathdefault mtight">i</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span><span class="mrel mtight">&#x2208;</span><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.02778em;">D</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.7026642857142857em;"><span style="top:-2.786em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mbin mtight">+</span></span></span></span></span></span></span></span></span></span></span><span style="top:-3.0000050000000003em;"><span class="pstrut" style="height:3em;"></span><span><span class="mop op-symbol small-op">&#x2211;</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:1.10797em;"><span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord">&#x2161;</span><span class="mopen">(</span><span class="mord mathdefault" style="margin-right:0.10764em;">f</span><span class="mopen">(</span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel"><span class="mrel"><span class="mord"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.69444em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="rlap"><span class="strut" style="height:0.8888799999999999em;vertical-align:-0.19444em;"></span><span class="inner"><span class="mrel">&#xE020;</span></span><span class="fix"></span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.19444em;"><span></span></span></span></span></span></span><span class="mrel">=</span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.03588em;">y</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:-0.03588em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mclose">)</span><span class="mord mathdefault">c</span><span class="mord mathdefault">o</span><span class="mord mathdefault">s</span><span class="mord"><span class="mord mathdefault">t</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">0</span><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mop op-limits"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.7500050000000003em;"><span style="top:-2.09213em;margin-left:0em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathdefault mtight">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3280857142857143em;"><span style="top:-2.357em;margin-left:0em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mathdefault mtight">i</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span><span class="mrel mtight">&#x2208;</span><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.02778em;">D</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.7026642857142857em;"><span style="top:-2.786em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mbin mtight">&#x2212;</span></span></span></span></span></span></span></span></span></span></span><span style="top:-3.0000050000000003em;"><span class="pstrut" style="height:3em;"></span><span><span class="mop op-symbol small-op">&#x2211;</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:1.10797em;"><span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord">&#x2161;</span><span class="mopen">(</span><span class="mord mathdefault" style="margin-right:0.10764em;">f</span><span class="mopen">(</span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel"><span class="mrel"><span class="mord"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.69444em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="rlap"><span class="strut" style="height:0.8888799999999999em;vertical-align:-0.19444em;"></span><span class="inner"><span class="mrel">&#xE020;</span></span><span class="fix"></span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.19444em;"><span></span></span></span></span></span></span><span class="mrel">=</span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.03588em;">y</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:-0.03588em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mclose">)</span><span class="mord mathdefault">c</span><span class="mord mathdefault">o</span><span class="mord mathdefault">s</span><span class="mord"><span class="mord mathdefault">t</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">1</span><span class="mord mtight">0</span></span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></p>
<ul>
<li><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mi>D</mi><mo>+</mo></msup></mrow><annotation encoding="application/x-tex">D^+</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.771331em;vertical-align:0em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.02778em;">D</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.771331em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mbin mtight">+</span></span></span></span></span></span></span></span></span></span></span>&#xFF1A;&#x5B9E;&#x4F8B;&#x96C6;<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>D</mi></mrow><annotation encoding="application/x-tex">D</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathdefault" style="margin-right:0.02778em;">D</span></span></span></span>&#x7684;&#x6B63;&#x4F8B;&#x5B50;&#x96C6;&#x3002;</li>
<li><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mi>D</mi><mo>&#x2212;</mo></msup></mrow><annotation encoding="application/x-tex">D^-</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.771331em;vertical-align:0em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.02778em;">D</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.771331em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mbin mtight">&#x2212;</span></span></span></span></span></span></span></span></span></span></span>&#xFF1A;&#x5B9E;&#x4F8B;&#x96C6;<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>D</mi></mrow><annotation encoding="application/x-tex">D</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathdefault" style="margin-right:0.02778em;">D</span></span></span></span>&#x7684;&#x53CD;&#x4F8B;&#x5B50;&#x96C6;&#x3002;</li>
</ul>
<h3 class="mume-header" id="%E4%BB%A3%E4%BB%B7%E6%9B%B2%E7%BA%BFcost-curve">&#x4EE3;&#x4EF7;&#x66F2;&#x7EBF;&#xFF08;Cost Curve&#xFF09;</h3>

<p>&#x6A2A;&#x8F74;&#x4E3A;&#x201C;<strong>&#x6B63;&#x6982;&#x7387;&#x4EE3;&#x4EF7;</strong>&#x201D;&#xFF0C;&#x7EB5;&#x8F74;&#x4E3A;&#x201C;<strong>&#x5F52;&#x4E00;&#x5316;&#x4EE3;&#x4EF7;</strong>&#x201D;&#x3002;</p>
<p><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>P</mi><mo stretchy="false">(</mo><mo>+</mo><mo stretchy="false">)</mo><mrow><mi>c</mi><mi>o</mi><mi>s</mi><mi>t</mi></mrow><mo>=</mo><mstyle displaystyle="true" scriptlevel="0"><mfrac><mrow><mi>p</mi><mo>&#x22C5;</mo><mi>c</mi><mi>o</mi><mi>s</mi><msub><mi>t</mi><mn>01</mn></msub></mrow><mrow><mi>p</mi><mo>&#x22C5;</mo><mi>c</mi><mi>o</mi><mi>s</mi><msub><mi>t</mi><mn>01</mn></msub><mo>+</mo><mo stretchy="false">(</mo><mn>1</mn><mo>&#x2212;</mo><mi>p</mi><mo stretchy="false">)</mo><mo>&#x22C5;</mo><mi>c</mi><mi>o</mi><mi>s</mi><msub><mi>t</mi><mn>10</mn></msub></mrow></mfrac></mstyle></mrow><annotation encoding="application/x-tex">P(+){cost} = \dfrac{
    p &#x22C5; cost_{01}
}{
    p &#x22C5; cost_{01}  + (1-p) &#x22C5; cost_{10} 
}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathdefault" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord">+</span><span class="mclose">)</span><span class="mord"><span class="mord mathdefault">c</span><span class="mord mathdefault">o</span><span class="mord mathdefault">s</span><span class="mord mathdefault">t</span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:2.22808em;vertical-align:-0.936em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.29208em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault">p</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">&#x22C5;</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathdefault">c</span><span class="mord mathdefault">o</span><span class="mord mathdefault">s</span><span class="mord"><span class="mord mathdefault">t</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">0</span><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mopen">(</span><span class="mord">1</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">&#x2212;</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathdefault">p</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">&#x22C5;</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathdefault">c</span><span class="mord mathdefault">o</span><span class="mord mathdefault">s</span><span class="mord"><span class="mord mathdefault">t</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">1</span><span class="mord mtight">0</span></span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault">p</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">&#x22C5;</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathdefault">c</span><span class="mord mathdefault">o</span><span class="mord mathdefault">s</span><span class="mord"><span class="mord mathdefault">t</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">0</span><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.936em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></p>
<ul>
<li><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi></mrow><annotation encoding="application/x-tex">p</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em;"></span><span class="mord mathdefault">p</span></span></span></span>&#xFF1A;&#x6837;&#x4F8B;&#x4E3A;&#x6B63;&#x4F8B;&#x7684;&#x6982;&#x7387;&#x3002;</li>
</ul>
<p><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>c</mi><mi>o</mi><mi>s</mi><msub><mi>t</mi><mrow><mi>n</mi><mi>o</mi><mi>r</mi><mi>m</mi></mrow></msub><mo>=</mo><mstyle displaystyle="true" scriptlevel="0"><mfrac><mrow><mi>F</mi><mi>N</mi><mi>R</mi><mo>&#x22C5;</mo><mi>p</mi><mo>&#x22C5;</mo><mi>c</mi><mi>o</mi><mi>s</mi><msub><mi>t</mi><mn>01</mn></msub><mo>+</mo><mi>F</mi><mi>P</mi><mi>R</mi><mo>&#x22C5;</mo><mo stretchy="false">(</mo><mn>1</mn><mo>&#x2212;</mo><mi>p</mi><mo stretchy="false">)</mo><mo>&#x22C5;</mo><mi>c</mi><mi>o</mi><mi>s</mi><msub><mi>t</mi><mn>10</mn></msub></mrow><mrow><mi>p</mi><mo>&#x22C5;</mo><mi>c</mi><mi>o</mi><mi>s</mi><msub><mi>t</mi><mn>01</mn></msub><mo>+</mo><mo stretchy="false">(</mo><mn>1</mn><mo>&#x2212;</mo><mi>p</mi><mo stretchy="false">)</mo><mo>&#x22C5;</mo><mi>c</mi><mi>o</mi><mi>s</mi><msub><mi>t</mi><mn>10</mn></msub></mrow></mfrac></mstyle></mrow><annotation encoding="application/x-tex">cost_{norm} = \dfrac{
    FNR &#x22C5; p &#x22C5; cost_{01} +
    FPR &#x22C5; (1-p) &#x22C5; cost_{10} 
}{
    p &#x22C5; cost_{01}  + (1-p) &#x22C5; cost_{10} 
}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.76508em;vertical-align:-0.15em;"></span><span class="mord mathdefault">c</span><span class="mord mathdefault">o</span><span class="mord mathdefault">s</span><span class="mord"><span class="mord mathdefault">t</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">n</span><span class="mord mathdefault mtight">o</span><span class="mord mathdefault mtight" style="margin-right:0.02778em;">r</span><span class="mord mathdefault mtight">m</span></span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:2.363em;vertical-align:-0.936em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.427em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault">p</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">&#x22C5;</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathdefault">c</span><span class="mord mathdefault">o</span><span class="mord mathdefault">s</span><span class="mord"><span class="mord mathdefault">t</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">0</span><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mopen">(</span><span class="mord">1</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">&#x2212;</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathdefault">p</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">&#x22C5;</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathdefault">c</span><span class="mord mathdefault">o</span><span class="mord mathdefault">s</span><span class="mord"><span class="mord mathdefault">t</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">1</span><span class="mord mtight">0</span></span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em;">F</span><span class="mord mathdefault" style="margin-right:0.10903em;">N</span><span class="mord mathdefault" style="margin-right:0.00773em;">R</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">&#x22C5;</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathdefault">p</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">&#x22C5;</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathdefault">c</span><span class="mord mathdefault">o</span><span class="mord mathdefault">s</span><span class="mord"><span class="mord mathdefault">t</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">0</span><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathdefault" style="margin-right:0.13889em;">F</span><span class="mord mathdefault" style="margin-right:0.13889em;">P</span><span class="mord mathdefault" style="margin-right:0.00773em;">R</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">&#x22C5;</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mopen">(</span><span class="mord">1</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">&#x2212;</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathdefault">p</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">&#x22C5;</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathdefault">c</span><span class="mord mathdefault">o</span><span class="mord mathdefault">s</span><span class="mord"><span class="mord mathdefault">t</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">1</span><span class="mord mtight">0</span></span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.936em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></p>
<ul>
<li><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>F</mi><mi>N</mi><mi>R</mi><mo>=</mo><mstyle displaystyle="true" scriptlevel="0"><mfrac><mrow><mi>F</mi><mi>N</mi></mrow><mrow><mi>T</mi><mi>r</mi><mi>u</mi><mi>e</mi></mrow></mfrac></mstyle></mrow><annotation encoding="application/x-tex">FNR = \dfrac{FN}{True}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathdefault" style="margin-right:0.13889em;">F</span><span class="mord mathdefault" style="margin-right:0.10903em;">N</span><span class="mord mathdefault" style="margin-right:0.00773em;">R</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:2.04633em;vertical-align:-0.686em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.36033em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em;">T</span><span class="mord mathdefault" style="margin-right:0.02778em;">r</span><span class="mord mathdefault">u</span><span class="mord mathdefault">e</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em;">F</span><span class="mord mathdefault" style="margin-right:0.10903em;">N</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></li>
<li><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>F</mi><mi>P</mi><mi>R</mi><mo>=</mo><mstyle displaystyle="true" scriptlevel="0"><mfrac><mrow><mi>F</mi><mi>P</mi></mrow><mrow><mi>F</mi><mi>a</mi><mi>l</mi><mi>s</mi><mi>e</mi></mrow></mfrac></mstyle></mrow><annotation encoding="application/x-tex">FPR = \dfrac{FP}{False}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathdefault" style="margin-right:0.13889em;">F</span><span class="mord mathdefault" style="margin-right:0.13889em;">P</span><span class="mord mathdefault" style="margin-right:0.00773em;">R</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:2.04633em;vertical-align:-0.686em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.36033em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em;">F</span><span class="mord mathdefault">a</span><span class="mord mathdefault" style="margin-right:0.01968em;">l</span><span class="mord mathdefault">s</span><span class="mord mathdefault">e</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em;">F</span><span class="mord mathdefault" style="margin-right:0.13889em;">P</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></li>
</ul>
<p><img src="./images/e_CostCurve.png" alt></p>
<h2 class="mume-header" id="%E6%AF%94%E8%BE%83%E6%A3%80%E9%AA%8C">&#x6BD4;&#x8F83;&#x68C0;&#x9A8C;</h2>

<p>&#x6211;&#x4EEC;&#x5E0C;&#x671B;&#x6BD4;&#x8F83;&#x7684;&#x662F;&#x6CDB;&#x5316;&#x6027;&#x80FD;&#xFF0C;&#x7136;&#x800C;&#x901A;&#x8FC7;&#x5B9E;&#x9A8C;&#x8BC4;&#x4F30;&#x65B9;&#x6CD5;&#x6211;&#x4EEC;&#x83B7;&#x5F97;&#x7684;&#x662F;&#x6D4B;&#x8BD5;&#x96C6;&#x4E0A;&#x7684;&#x6027;&#x80FD;&#xFF0C;&#x4E24;&#x8005;&#x7684;&#x5BF9;&#x6BD4;&#x7ED3;&#x679C;&#x672A;&#x5FC5;&#x76F8;&#x540C;&#x3002;</p>
<table>
<thead>
<tr>
<th style="text-align:center">&#x6BD4;&#x8F83;&#x7B97;&#x6CD5;&#x6570;&#x91CF;</th>
<th style="text-align:center">&#x68C0;&#x9A8C;&#x540D;&#x79F0;</th>
<th style="text-align:left">&#x8BF4;&#x660E;</th>
</tr>
</thead>
<tbody>
<tr>
<td style="text-align:center">2</td>
<td style="text-align:center">&#x4EA4;&#x53C9;&#x9A8C;&#x8BC1;<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>t</mi></mrow><annotation encoding="application/x-tex">t</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.61508em;vertical-align:0em;"></span><span class="mord mathdefault">t</span></span></span></span>&#x68C0;&#x9A8C;</td>
<td style="text-align:left"></td>
</tr>
<tr>
<td style="text-align:center">2</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>M</mi><mi>c</mi><mi>N</mi><mi>e</mi><mi>m</mi><mi>a</mi><mi>r</mi></mrow><annotation encoding="application/x-tex">McNemar</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathdefault" style="margin-right:0.10903em;">M</span><span class="mord mathdefault">c</span><span class="mord mathdefault" style="margin-right:0.10903em;">N</span><span class="mord mathdefault">e</span><span class="mord mathdefault">m</span><span class="mord mathdefault">a</span><span class="mord mathdefault" style="margin-right:0.02778em;">r</span></span></span></span>&#x68C0;&#x9A8C;</td>
<td style="text-align:left"></td>
</tr>
<tr>
<td style="text-align:center">*</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>F</mi><mi>r</mi><mi>i</mi><mi>e</mi><mi>n</mi><mi>d</mi><mi>m</mi><mi>a</mi><mi>n</mi></mrow><annotation encoding="application/x-tex">Friendman</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.69444em;vertical-align:0em;"></span><span class="mord mathdefault" style="margin-right:0.13889em;">F</span><span class="mord mathdefault" style="margin-right:0.02778em;">r</span><span class="mord mathdefault">i</span><span class="mord mathdefault">e</span><span class="mord mathdefault">n</span><span class="mord mathdefault">d</span><span class="mord mathdefault">m</span><span class="mord mathdefault">a</span><span class="mord mathdefault">n</span></span></span></span>&#x68C0;&#x9A8C;</td>
<td style="text-align:left"></td>
</tr>
<tr>
<td style="text-align:center">*</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>N</mi><mi>e</mi><mi>m</mi><mi>e</mi><mi>n</mi><mi>y</mi><mi>i</mi></mrow><annotation encoding="application/x-tex">Nemenyi</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8777699999999999em;vertical-align:-0.19444em;"></span><span class="mord mathdefault" style="margin-right:0.10903em;">N</span><span class="mord mathdefault">e</span><span class="mord mathdefault">m</span><span class="mord mathdefault">e</span><span class="mord mathdefault">n</span><span class="mord mathdefault" style="margin-right:0.03588em;">y</span><span class="mord mathdefault">i</span></span></span></span>&#x540E;&#x7EED;&#x68C0;&#x9A8C;</td>
<td style="text-align:left"></td>
</tr>
</tbody>
</table>
<h2 class="mume-header" id="%E5%81%8F%E5%B7%AE">&#x504F;&#x5DEE;</h2>

<p><strong>&#x504F;&#x5DEE;</strong></p>
<p><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>b</mi><mi>i</mi><mi>a</mi><msub><mi>s</mi><mi>i</mi></msub><mo>=</mo><mi>f</mi><mo stretchy="false">(</mo><msub><mi>x</mi><mi>i</mi></msub><mo stretchy="false">)</mo><mo>&#x2212;</mo><msub><mi>y</mi><mi>i</mi></msub></mrow><annotation encoding="application/x-tex">bias_i = f(x_i) - y_i</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.84444em;vertical-align:-0.15em;"></span><span class="mord mathdefault">b</span><span class="mord mathdefault">i</span><span class="mord mathdefault">a</span><span class="mord"><span class="mord mathdefault">s</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathdefault" style="margin-right:0.10764em;">f</span><span class="mopen">(</span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">&#x2212;</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.03588em;">y</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:-0.03588em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span></span></p>
<p><strong>&#x65B9;&#x5DEE;</strong></p>
<p><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mi>&#x3B5;</mi><mn>2</mn></msup><mo>=</mo><mfrac><mrow><munderover><mo>&#x2211;</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mi>m</mi></munderover><msup><mrow><mi>b</mi><mi>i</mi><mi>a</mi><msub><mi>s</mi><mi>i</mi></msub></mrow><mn>2</mn></msup></mrow><mi>m</mi></mfrac></mrow><annotation encoding="application/x-tex">&#x3B5;^2 = \dfrac{ 
    \sum\limits_{i=1}^{m} {bias_i}^2
 }{m}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8641079999999999em;vertical-align:0em;"></span><span class="mord"><span class="mord mathdefault">&#x3B5;</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8641079999999999em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:3.4050659999999997em;vertical-align:-0.686em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.7190659999999998em;"><span style="top:-2.6653970000000005em;"><span class="pstrut" style="height:3.3513970000000004em;"></span><span class="mord"><span class="mord mathdefault">m</span></span></span><span style="top:-3.5813970000000004em;"><span class="pstrut" style="height:3.3513970000000004em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-4.719066em;"><span class="pstrut" style="height:3.3513970000000004em;"></span><span class="mord"><span class="mop op-limits"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.3513970000000004em;"><span style="top:-2.122331em;margin-left:0em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span><span class="mrel mtight">=</span><span class="mord mtight">1</span></span></span></span><span style="top:-3.0000050000000003em;"><span class="pstrut" style="height:3em;"></span><span><span class="mop op-symbol small-op">&#x2211;</span></span></span><span style="top:-3.950005em;margin-left:0em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">m</span></span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.9776689999999999em;"><span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord"><span class="mord"><span class="mord mathdefault">b</span><span class="mord mathdefault">i</span><span class="mord mathdefault">a</span><span class="mord"><span class="mord mathdefault">s</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8984479999999999em;"><span style="top:-3.1473400000000002em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></p>
<h3>&#x504F;&#x5DEE;&#x65B9;&#x5DEE;&#x7A98;&#x5883;&#xFF08;Bias-Variance Dilemma&#xFF09;</h3>
<p>&#x4E00;&#x822C;&#x6765;&#x8BF4;&#xFF0C;&#x504F;&#x5DEE;&#x4E0E;&#x65B9;&#x5DEE;&#x662F;&#x6709;&#x51B2;&#x7A81;&#x7684;&#xFF0C;&#x5047;&#x5B9A;&#x6211;&#x4EEC;&#x80FD;&#x63A7;&#x5236;&#x5B66;&#x4E60;&#x7B97;&#x6CD5;&#x7684;&#x8BAD;&#x7EC3;&#x7A0B;&#x5EA6;&#xFF0C;&#x5219;&#x5728;&#x8BAD;&#x7EC3;&#x4E0D;&#x8DB3;&#x65F6;&#xFF0C;&#x5B66;&#x4E60;&#x5668;&#x7684;&#x62DF;&#x5408;&#x80FD;&#x529B;&#x4E0D;&#x591F;&#x5F3A;&#xFF0C;&#x8BAD;&#x7EC3;&#x6570;&#x636E;&#x7684;&#x6270;&#x52A8;&#x4E0D;&#x8DB3;&#x4EE5;&#x4F7F;&#x5B66;&#x4E60;&#x5668;&#x4EA7;&#x751F;&#x663E;&#x8457;&#x53D8;&#x5316;&#xFF0C;&#x6B64;&#x65F6;&#x504F;&#x5DEE;&#x4E3B;&#x5BFC;&#x4E86;&#x6CDB;&#x5316;&#x9519;&#x8BEF;&#x7387;&#xFF1B;&#x968F;&#x7740;&#x8BAD;&#x7EC3;&#x7A0B;&#x5EA6;&#x7684;&#x52A0;&#x6DF1;&#xFF0C;&#x5B66;&#x4E60;&#x5668;&#x7684;&#x62DF;&#x5408;&#x80FD;&#x529B;&#x9010;&#x6E10;&#x589E;&#x5F3A;&#xFF0C;&#x8BAD;&#x7EC3;&#x6570;&#x636E;&#x53D1;&#x751F;&#x7684;&#x6270;&#x52A8;&#x6E10;&#x6E10;&#x80FD;&#x88AB;&#x5B66;&#x4E60;&#x5668;&#x5B66;&#x5230;&#xFF0C;&#x65B9;&#x5DEE;&#x9010;&#x6E10;&#x4E3B;&#x5BFC;&#x4E86;&#x6CDB;&#x5316;&#x9519;&#x8BEF;&#x7387;&#x3002;</p>
<p><img src="./images/e_BVD.png" alt></p>

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